Once the initial batch of enemies are taken out at the pit, follow Price and attack the next chamber from the lower path (more cover). Down the RPG soldiers near the mining rigging and work your way across. The control to the side is a good place to secure, as there is only one way for enemies to enter.

After cutting into the last mining chamber, you will be on the way to the next section. Deal with the RPG soldiers in the small room and get to the exit stairs (the ones going up).

Cross the Pit

Refill on the ammunition box right before exiting the mines to cross the stripmine pit. You may not need the ammo in the next section, but you will in the section after the pit.

Head out to the pit, but hide in an open cargo container. You will be given control of a OCVA soon and can literally wipe out the enemies in the pit without really firing a shot on your own.

Cross from the first half of the mining pit to the second (via construction yard). Use the pipes as cover, and head for the two story shed in the distance. The reason to take cover is that your UCAV will be downed, and you will need to snipe at enemies from cover. If you don't fire from cover, you will be KIA'd very fast. Clear the field, then walk to the destroyed bunker entrance.

Rescue the Hostages

Head past Alena's room and try to nuke or grenade the bridge where all the enemies are. Once you manage to quiet them down, you can rappel off the bridge and continue your pursuit.

The lowest level of the mine tunnel is murderous since you need to make constant progress (or the bad guys escape with the President, and you fail). Take out the rocket soldiers on the overhead walkway and move forwards. Once you've cleared most of the path and reached the stairs near the marked double doors, enemies tend to fade away.

Reload your weapons before setting the charges as indicated by Price. Use the slow-motion effect to down the enemies near the hostage, and use a carefully placed headshot to whack the hostage taker.

Defend Until Evac Arrives

Defend the president by going prone and zapping enemies. You have to fulfill a kill quota before the chopper comes in, so get to it. Taking out enemies also makes it easier to make your way to the chopper once it has landed. Once Yuri gets taken out by the explosion, you pretty much finish the level ... just bear with the cinematic bullstuff that occurs afterward.